I've been looking at old houses on the east side (1,100-1,500 square feet), and even for those houses on small lots, it's hard to find anything less than $450K, and many that I've looked at listed in the low $400's need close to six figures worth of structural work and repairs (and with current rates, low $400's isn't really doable without a huge salary). It's crazy. Many of even these smaller houses in decent, unimproved condition on the east side of the Salt Lake Valley are listed in excess of half a million dollars.
It takes a very long time of saving to be able to crack into that price range with a median or slightly above median income.